Question

log baza 2din x +log baza2 din(x+1)=log baza
2 din 2

Answer 1

$log_2 \ x + log_2 \ (x+1)= log_2 \ 2 \\\\ \hbox{Se pun conditiile de existenta a radicalilor pentru fiecare in parte} : \\\\\\ x\ \textgreater \ 0 \to x \in (0; + \infty) \\\\ x+1\ \textgreater \ 0 \ \ \ \textless \ =\ \textgreater \ x\ \textgreater \ -1 \to x \in (-1; + \infty) \\\\ (0; + \infty) \bigcap (-1; \infty) \longrightarrow x \in (0; \infty) \\\\ log_2 \ x(x+1)=log_2 \ 2 \\\\\\ x(x+1)=2 \\\\ x^2+x=2 \\\\ x^2+x-2=0 \\\\ \Delta=1-4*(-2)=1+8 \to 9$


$x_1=\frac{-1+3}{2}=\frac{\not 2}{\not 2} \to 1\\\\ x_2=\frac{-1-3}{2} = \frac{- \not 4}{\not 2} \to -2 \\\\ x \in (0; \infty) \\\\\\ \Longrightarrow S_x= \{1\}$